Question: Rewrite as a simplified fraction. ${3.13\overline{6} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 3136.6666...\\ 100x &= 313.6666...\end{align*}}$ Subtracting the two equations, we have: ${900x = 2823}$ ${x = \dfrac{2823}{900}} $ ${x = \dfrac{941}{300}} \text{or} {3 \dfrac{41}{300}}$